 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            Session 4:
Homework  Problem H1 Lines p and q are parallel. Find the measures of all of the numbered angles. Explain how you found each measure.  Problem H2 No matter which triangle you start with, you can extend the three sides and add a line parallel to one side. In the following problems, do not use your protractor or anything else to measure the angles. Instead, look at the above picture and use what you know about lines and angles.

 a. In the picture above, what is m 1 + m 2 + m 3? Explain how you got your answer. b. In the picture above, 1 is the equal in measure to one of the angles in the triangle. Which one? c. In the picture above, 2 is the equal in measure to one of the angles in the triangle. Which one? d. In the picture above, 3 is the equal in measure to one of the angles of the triangle. Which one? e. Use your answers to questions (a)-(d) to explain why m 4 + m 5 + m 6 is 180°. Explain why this would be true for any triangle, and not just the one pictured. Problem H3 A central angle is an angle with its vertex at the center of a circle: a. If the central angle cuts off a quarter-circle, what is the measure of the central angle? b. If the central angle cuts off a semicircle, what is the measure of the central angle? c. If the central angle cuts off one-third of a circle, what is the measure of the central angle? d. Find a general rule for central angles based on how much of the circle they cut off. Problem H4 In the below figure, a central angle and an inscribed angle cut off (intercept) the same arc of a circle: a. Make a conjecture: Which of the two angles is larger? b. How much larger is it? c. How did you make your decision?     Cuoco, Al; Goldenberg, E. Paul; and Mark, June (December, 1996). Geometric Approaches to Things. In the paper "Habits of Mind: An Organizing Principle for Mathematics Curriculum." The Journal of Mathematical Behavior, 5, (4), pp. 375-402.    Session 4: Index | Notes | Solutions | Video